How do you simplify #4 sqrt 3 - sqrt 64 + 6 sqrt 27#?

Question

Eva Adamson · Accepted Answer

#22sqrt3−8# We know that #sqrt 64 = 8#, so we have #4sqrt3−8+6sqrt27# Now let's rewrite #sqrt27# as #sqrt(9)*sqrt3# since we know the square root of 9, we can write it as #3sqrt3# Now just a bit of simple multiplication and combining link terms #4sqrt3−8+6(3sqrt3)# #4sqrt3−8+18sqrt3)# #22sqrt3−8#

Ethan Adkins · Answer

22sqrt[3] -8

We can simplify first by solving sqrt[64] since we know it is a perfect square. This leaves: 4sqrt[3] -8 + 6sqrt[27] Then we need to see if we can simplify the square roots. 4sqrt[3] is as simplified as it gets. 6sqrt[27] can be broken up into factors so: 6sqrt[27] = 6sqrt[3*9] 9 is a perfect square so it can be rooted and brought out side of the square root. This leaves: 6(3)sqrt[3] So now we have: 4sqrt[3] -8 + 18sqrt[3] Combine terms: 22sqrt[3] - 8

Jace Anderson · Answer

undefined To simplify the expression 4√3 - √64 + 6√27, we can simplify each square root separately and then combine like terms.

First, simplify √64. The square root of 64 is 8, so we have 4√3 - 8 + 6√27.

Next, simplify √27. The square root of 27 is 3√3, so we have 4√3 - 8 + 6(3√3).

Now, multiply 6 by 3√3 to get 18√3. We have 4√3 - 8 + 18√3.

Finally, combine like terms. 4√3 and 18√3 are like terms, so we add them together to get 22√3. We have 22√3 - 8.

Therefore, the simplified expression is 22√3 - 8.